# Urban Flood Detection with Sentinel-1 Multi-Temporal Synthetic Aperture Radar (SAR) Observations in a Bayesian Framework: A Case Study for Hurricane Matthew

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## Abstract

**:**

## 1. Introduction

^{0}, log intensity in dB) decreases due to the specular surface of open flood waters if radar energy is mostly forward-scattered. In other cases, σ

^{0}may increase if the radar wave bounces first off the water surface (away from the satellite) and then off a semivertical structure, such as a building wall, tree trunk, or even a car in the flood (towards the satellite); this is the “double bounce” effect. Compared with rural floods, urban flood mapping suffers more from layover and shadow effects due to SAR’s side-looking nature. The layover zone is in front of buildings, toward the satellite direction, and the length is usually longer than the building height at incidence angles lower than 45° (layover length = building height × cot(incidence angle) [2]). Within this zone there is a good chance of seeing stronger backscattering due to the double bounce effect, and its strength is a function of the oblique angle between the flight direction and the building orientation. The double-bounce intensity increase can be larger than 10 dB at 0° and remains high up to 5°; at an angle larger than 10° the increase will drop to a constant level [3,4]. The shadow zone, on the other hand, has a smaller length (shadow length = building height × tan(incidence angle) [2]), and the backscattering stays low at all times. The low intensity within the shadow may lead to false flood detection if one uses a during-flood SAR image alone.

## 2. Study Area and Data

#### 2.1. Study Area and Weather Event

#### 2.2. Optical and Synthetic Aperture Radar (SAR) Imagery

## 3. Data Processing and Analysis

#### 3.1. Validation Dataset

^{0}responses based on different land cover types. We manually classified the during-flood aerial image into the following six classes (Table 1 and Figure 2):

^{0}tended to stay low both in the non- and during-event images given the constant specular reflection surface at all times.

^{0}. If the tree crown was too dense to penetrate, SAR σ

^{0}stayed relatively stable with potential seasonal variations.

^{0}should also stay at a relatively constant level with potential seasonal variations.

^{0}may stay at a relatively high level due to the dense tree tops, but the actual level and the during-event response may vary within the same forest patch. We did not include pixels in this class in the final confusion matrix calculation.

#### 3.2. Sentinel-1 SAR Data Processing

^{0}) in decibels (dB) by the following definition:

^{0}values on a pixel-by-pixel basis in the following multitemporal analysis.

#### 3.3. SAR Intensity Time Series

^{0}slightly varied with time but mostly stayed low, around −20 dB (Figure 4a; sample pixel 2 in Figure 2). In some epochs the value may go 5 dB higher, close to some of the nonflooded epochs in the flood class. This natural variation may be associated with the changes of floating aquatic plants in the pond, which can be observed in the WorldView/QuickBird images in Google Earth.

^{0}values between −5 and −8 dB in general, with the Dry Vegetation class higher on average than the other (Figure 4b). This difference may simply represent different vegetation density or structures between two sample pixels. The more important difference was the intensity increase (~3 dB) in the time series of the Flooded Vegetation class on the during-event epoch, revealing possible double-bounce backscattering between the tree and flood water surfaces.

^{0}values for Dry class (sample pixel 5) stayed at a constant low level around −15 dB, even more stable than the Permanent Water sample pixel (Figure 4c). This pattern reflects the characteristics of paved road (Figure 2a,b), with the asphalt layer showing low backscattering intensity. We also examined another pixel in the Dry class (sample pixel 5-1), and the values fluctuated within a wider range, possibly due to the changes between land cover type (bare ground vs. lawn) and/or changes in soil moisture. Regardless of different temporal patterns in these two sample pixels, neither of them showed any intensity anomalies for the during-event epoch.

**Figure 4.**(

**a**–

**c**) σ

^{0}time series of selected pixels for the 6 classes in the validation dataset. The location of each sample pixel is marked in Figure 2, with the same ID number as shown in the legend (e.g., “1-Flood” in the legend of Figure 4a is from the sample pixel 1 in Figure 2). The grey bars in the background are 3-day cumulative precipitation from Global Precipitation Measurement daily solutions [26]. The during-event epoch is marked by the precipitation record of >250 mm. (

**d**–

**f**) Histogram of the time series. The vertical lines stand for the σ

^{0}values on the during-event epoch. (

**g**–

**i**) Histogram of normalized time series. Vertical lines stand for the during-event σ

^{0}values after normalization.

^{0}values for the Uncertain class seemed to show low-frequency seasonal variations between the years of 2017 and 2018. As the pixel was located in the middle of a dense forest (sample pixel 6), the undulations in the time series may reflect seasonal changes in the forest.

^{0}for each of the time series. In Figure 4d, we can see that the histogram for the Flood and Permanent Water classes looked very different, but their during-event σ

^{0}values were almost identical. For the Flooded Vegetation and Dry Vegetation classes (Figure 4e), however, the histograms were more similar, with also small differences in the σ

^{0}values on the during-event epoch. Figure 4d,e together demonstrated that, in general, it was easier to map out the open-water flood, whereas the double-bounce effect associated with flooded vegetation cannot be easily identified. Given the high-frequency variation of σ

^{0}values in almost every class, plus a much smaller during-event σ

^{0}change in the Flooded Vegetation class than that in the Flood class, identifying the double bounce effect in the SAR image will never be an easy task.

## 4. Methods

#### 4.1. Probabilistic Thesholding on Normalized Intensity Time Series

- (1)
- Compute the mean (μ
_{ts}) and standard deviation (S_{ts}) of σ^{0}from nonflood epochs in the time series by excluding the during-event (k^{th}) epoch:$${\mu}_{ts}=\frac{{{\displaystyle \sum}}_{i=1}^{n}{\sigma}_{i}^{0}}{n}{S}_{ts}^{2}=\frac{{{\displaystyle \sum}}_{i=0}^{n}{\left({\sigma}_{i}^{0}-{\mu}_{ts}\right)}^{2}}{n-1}wherei=1,2,\dots ,nandi\ne k$$ - (2)
- Normalize the whole time series, including the during-event k
^{th}epoch:$$\tilde{{\sigma}_{i}^{0}}=\frac{{\sigma}_{i}^{0}-{\mu}_{ts}}{{S}_{ts}}$$This was the most critical step in our approach. The normalized intensities are read as the deviation from their ordinary state (the historical mean) on the same scale (after being divided by the time series standard deviation). The normalized during-event intensity can indicate how anomalous it is from all the other pre-event epochs after considering the natural variations. When we look at the histogram after normalization, the curve will be centered at zero (Figure 4g–i), with the normalized during-event intensity being at either the left or right far end of the distribution due to the presence of specular reflection or double bounce. As mentioned in Section 3.3, the histogram actually reflects the probability of mainly the nonflooded condition. To honor the fact that the flooded condition should also have its own probability, next we tried to incorporate the Bayesian approach into our method. - (3)
- With the normalized time series, for each pixel, construct the conditional probability of an epoch to be flooded, using the following equation:$$p\left(F|\tilde{{\sigma}_{i}^{0}}\right)=\frac{p(\tilde{{\sigma}_{i}^{0}}|F)p\left(F\right)}{p\left(\tilde{{\sigma}_{i}^{0}}|F\right)p\left(F\right)+p(\tilde{{\sigma}_{i}^{0}}|\overline{F})p\left(\overline{F}\right)}$$$$p\left(\tilde{{\sigma}_{i}^{0}}|F\right)=\frac{1}{\sqrt{2\pi {s}_{F}}}exp[-\frac{1}{2}\frac{{(\tilde{{\sigma}_{i}^{0}}-{m}_{F})}^{2}}{{s}_{F}^{2}}]$$$$p\left(\tilde{{\sigma}_{i}^{0}}|\overline{F}\right)=\frac{1}{\sqrt{2\pi {s}_{\overline{F}}}}exp[-\frac{1}{2}\frac{{(\tilde{{\sigma}_{i}^{0}}-{m}_{\overline{F}})}^{2}}{{s}_{\overline{F}}^{2}}]$$$$h\left(y\right)={G}_{1}+{G}_{2}+{G}_{3}={A}_{1}exp\left[-\frac{1}{2}\frac{{\left(y-{m}_{1}\right)}^{2}}{{s}_{1}^{2}}\right]+{A}_{2}exp\left[-\frac{1}{2}\frac{{\left(y-{m}_{2}\right)}^{2}}{{s}_{2}^{2}}\right]\phantom{\rule{0ex}{0ex}}+{A}_{3}exp\left[-\frac{1}{2}\frac{{\left(y-{m}_{3}\right)}^{2}}{{s}_{3}^{2}}\right]$$The third Gaussian curve fits the bulging part at the high end of the histogram and, hence, gives lower root-mean-square errors compared with the two-Gaussian model (Figure 5a,b). We used the parameters for the Gaussian curves on the left and on the right (Figure 5a), (m
_{1}, s_{1}) and (m_{3}, s_{3}), to approximate the ${m}_{F}$ and ${s}_{F}$ in the likelihood functions for the pixels of intensity decrease (${p}_{D}\left(\tilde{{\sigma}_{i}^{0}}|\overline{F}\right)$) and intensity increase (${p}_{U}\left(\tilde{{\sigma}_{i}^{0}}|\overline{F}\right)$) respectively (Figure 5c). From here we can construct the conditional probability function for each case separately (denoted as ${p}_{D}$ and ${p}_{U}$ in Figure 5d using (4). - (4)
- Generate the flood probability map for the during-event epoch (k
^{th}) by putting $\tilde{{\sigma}_{k}^{0}}$ in ${p}_{D}$ and ${p}_{U}$. We can also define a probability cutoff value and form a binary flood map. In this case, we adopted $p=0.5,$ which has been identified to be associated with the transition zone [29]. Next we will describe the validation process using this binary flood map.

#### 4.2. Validation Approach

## 5. Results

^{0}thresholds spatially varied.

## 6. Discussion

^{0}decrease and 18% with σ

^{0}increase. In the remaining 50% there was no clear σ

^{0}anomaly based on the thresholds given. In the Flooded Vegetation class, we saw more pixels with σ

^{0}increase (18%) than those with σ

^{0}decrease (12%). However, about 70% of the pixels in the Flooded Vegetation class did not see significant σ

^{0}changes. In the Permanent Water class, 22% of the pixels were identified as flood by σ

^{0}decrease. As for the Dry and Dry Vegetation classes, we saw a small fraction of false positives (6%–10%). Next, we would like to address the potential sources that cause the underprediction in the Flood and Flooded Vegetation class as well as the overprediction in the Permanent Water and Dry class.

#### 6.1. Uncertainties in the Validation Dataset

#### 6.2. Source of Underprediction

#### 6.3. Source of Overprediction

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Lumberton in Robeson County, North Carolina, and the during-event airborne optical imagery taken on 11 October 2016. The Lumber River flows right through the middle of the town. USC00315177 is National Oceanic and Atmospheric Administration (NOAA)’s ground weather station.

**Figure 2.**(

**a**) The during-event aerial image and (

**b**) the validation vector image with 30 cm resolution. (

**c**) The rasterized validation image at 15 m resolution. (

**d**) The during-event Sentinel-1 synthetic aperture radar (SAR) image at 15 m posting. The cyan box indicates the region used for Gaussian curve fitting. (

**e**,

**f**) The magnified views of (

**a**–

**d**) for the urban area. The open circles labeled 1 to 6 in (

**b**) are the sample pixels of the time series (Figure 4) for each class.

**Figure 3.**The processing flow chart for the intensity stack and flood proxy map. JPL ISCE, Jet Propulsion Laboratory’s InSAR Scientific Computing Environment.

**Figure 5.**(

**a**) The histogram and 2-Gaussian curve fitting for the during-event epoch in the normalized time series. (

**b**) The curve fitting for 3-Gaussian model. RMSE = root-mean-square error. (

**c**) The probability for the nonflooded, the flooded with intensity decrease, and the flooded cases, with intensity increase for the normalized backscattering in the time series. (

**d**) The conditional probability of the normalized backscattering in the time series being flooded with intensity decrease (blue curve) or intensity increase (cyan curve). Black line with arrow indicates the cutoff threshold of p = 0.5 for a binary flood map.

**Figure 6.**Flood mapped by the probability threshold of p = 0.5 for (

**a**) the whole area of interest (AOI) and

**(b)**the urban area. The second and third panels are for the probability maps of (

**c**–

**d**) intensity decrease (${p}_{D}$) and (

**e**–

**f**) intensity increase (${p}_{U}$). Numbers in white circles are the patch IDs used in discussion.

**Figure 7.**Comparison between (

**a**) the contingency map obtained by $p=0.5$ cutoff threshold and (

**b**) the contingency map from the best result of grid search on log intensity ratio of during- and pre-event image (i.e., nontemporal analysis). Pixels in the Uncertain class are masked out from the map.

**Figure 8.**The reliability diagram between the flood probability ${p}_{F}$ and the observed frequency ${p}_{o}$ (white circles). The number of pixels for each probability bin is shown in vertical bars color-coded by contingency types. The deviation of the circles from the 1:1 line represents the error for each probability bin. The pixel counts in different contingency types shows that the error comes from FN (underprediction) for probability bins below 0.5, and FP (overprediction) for probability bins above 0.5.

**Figure 9.**The histogram comparison between the pixels in the Dry class and mapped as nonflooded (grey), Flood class and mapped as flooded with intensity decrease (cyan, interpreted as open water flood), and Flood class and mapped as flood with intensity increase (cyan, interpreted as double bounce scattering). (

**a**) Histogram for the pixel during-event intensity. (

**b**) Histogram for the pixel log intensity ratio. (

**c**) Histogram for the pixel during-event intensity after time-series normalization.

**Figure 10.**Pie charts showing, for each of the 6 classes, the proportions of pixels detected as flooded with either σ

^{0}decrease (blue) or σ

^{0}increase (yellow), or as nonflooded with insignificant σ

^{0}change at the p50 thresholds.

**Figure 11.**The during-event aerial photo for patch 1 (see Figure 6a for location), overlaid with (

**a**) the land cover classes in vector format, and (

**b**) the rasterized land cover map in 15 × 15m resolution. (

**c**) The pre-event satellite image overlaid with the Dry class for reference. The white dashed lines represent asphalt driveways. (

**d**) The contingency map for the Flood class. (

**e**) The contingency map for the Flooded Vegetation class.

**Figure 13.**The (

**a**) pre-event optical image and (

**b**) during-event aerial photo for patch 3. See Figure 6a for location. (

**c**) The contingency map for the Flood class. (

**d**–

**e**) Same as (

**a**–

**b**) for patch 4. (

**f**) The contingency map for the Dry class.

Responses in During-Event Scene | ||||
---|---|---|---|---|

Intensity Drop | Intensity Increase | Intensity Stays Low | Intensity Stays High | |

Flooded | Flood | Flood | ||

Flooded Vegetation | ||||

Nonflooded | Permanent Water | Dry Vegetation | ||

Dry | Dry | |||

Not Determined | Uncertain (not considered in evaluation metric) |

Type | Overall | Urban | ||||||
---|---|---|---|---|---|---|---|---|

CSI^{+} [%] | OA^{+} [%] | PA^{+} [%] | UA^{+} [%] | CSI [%] | OA [%] | PA [%] | UA [%] | |

p50-ts method | 34.4 | 80.8 | 45.5 | 56.7 | 40.2 | 42.8 | 43.4 | 83.3 |

Best result of grid search* on normalized ${\sigma}^{0}$ | 34.1 | 80.7 | 46.4 | 56.2 | 40.1 | 42.9 | 43.0 | 83.8 |

Best result of grid search* on log intensity ratio | 24.0 | 64.2 | 51.9 | 30.5 | 41.3 | 44.6 | 44.3 | 85.2 |

p50-ts method (treating Flooded Veg. as nonflooded) | 33.0 | 82.7 | 50.0 | 48.7 | 36.0 | 49.4 | 41.2 | 72.2 |

^{+}CSI = critical success index; OA = overall accuracy; PA = producer’s accuracy; UA = user’s accuracy

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## Share and Cite

**MDPI and ACS Style**

Lin, Y.N.; Yun, S.-H.; Bhardwaj, A.; Hill, E.M. Urban Flood Detection with Sentinel-1 Multi-Temporal Synthetic Aperture Radar (SAR) Observations in a Bayesian Framework: A Case Study for Hurricane Matthew. *Remote Sens.* **2019**, *11*, 1778.
https://doi.org/10.3390/rs11151778

**AMA Style**

Lin YN, Yun S-H, Bhardwaj A, Hill EM. Urban Flood Detection with Sentinel-1 Multi-Temporal Synthetic Aperture Radar (SAR) Observations in a Bayesian Framework: A Case Study for Hurricane Matthew. *Remote Sensing*. 2019; 11(15):1778.
https://doi.org/10.3390/rs11151778

**Chicago/Turabian Style**

Lin, Yunung Nina, Sang-Ho Yun, Alok Bhardwaj, and Emma M. Hill. 2019. "Urban Flood Detection with Sentinel-1 Multi-Temporal Synthetic Aperture Radar (SAR) Observations in a Bayesian Framework: A Case Study for Hurricane Matthew" *Remote Sensing* 11, no. 15: 1778.
https://doi.org/10.3390/rs11151778